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Speaker Series: Boris Kment, Princeton University

Title: "Ground and Paradox"

 

Abstract: This paper discusses a cluster of interrelated paradoxes, including those of set theory (e.g. Russell’s paradox), truth (e.g. the Liar), and the theory of properties (e.g. the paradox of heterologicality). I argue that an independently motivated theory of metaphysical grounding provides philosophically satisfying treatments of these paradoxes. It yields as corollaries a version of the iterative conception of set (which underlies the standard axiomatic set theory ZFC), and a solution to the property-theoretic paradoxes that rests on rejecting the law of excluded middle. The latter solution also applies to the paradoxes of truth, which can be subsumed under the property-theoretic ones. The treatment of the property-theoretic paradoxes has structural similarities to Kripke’s approach to the Liar and promises to resolve outstanding difficulties for this position, including revenge cases.